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Algebraic Graph Theory

Algebraic Graph Theory

2nd Edition

Part of Cambridge Mathematical Library

  • Author: Norman Biggs, London School of Economics and Political Science
  • Date Published: February 1994
  • availability: Available
  • format: Paperback
  • isbn: 9780521458979


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About the Authors
  • This is a substantial revision of a much-quoted monograph, first published in 1974. The structure is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of 'Additional Results' are included at the end of each chapter, thereby covering most of the major advances in the last twenty years. Professor Biggs' basic aim remains to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first part, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject which has strong links with the 'interaction models' studied in theoretical physics, and the theory of knots. The last part deals with symmetry and regularity properties. Here there are important connections with other branches of algebraic combinatorics and group theory. This new and enlarged edition this will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists.

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    Product details

    • Edition: 2nd Edition
    • Date Published: February 1994
    • format: Paperback
    • isbn: 9780521458979
    • length: 216 pages
    • dimensions: 225 x 158 x 14 mm
    • weight: 0.32kg
    • contains: 18 b/w illus.
    • availability: Available
  • Table of Contents

    1. Introduction to algebraic graph theory
    Part I. Linear Algebra in Graphic Thoery:
    2. The spectrum of a graph
    3. Regular graphs and line graphs
    4. Cycles and cuts
    5. Spanning trees and associated structures
    6. The tree-number
    7. Determinant expansions
    8. Vertex-partitions and the spectrum
    Part II. Colouring Problems:
    9. The chromatic polynomial
    10. Subgraph expansions
    11. The multiplicative expansion
    12. The induced subgraph expansion
    13. The Tutte polynomial
    14. Chromatic polynomials and spanning trees
    Part III. Symmetry and Regularity:
    15. Automorphisms of graphs
    16. Vertex-transitive graphs
    17. Symmetric graphs
    18. Symmetric graphs of degree three
    19. The covering graph construction
    20. Distance-transitive graphs
    21. Feasibility of intersection arrays
    22. Imprimitivity
    23. Minimal regular graphs with given girth

  • Author

    Norman Biggs, London School of Economics and Political Science

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